12 CHAPTER 1 STRUCTURE AND BONDING 15 sp3 Hybrid Orbitals and the Structure of Methane The bonding in the hydrogen molecule is fairly straightforward.but the situa tion is more complicated in organic molecules with tetravalent carbon atoms Take methane,CHa,for instance.As we've seen,carbon has four valence elec trons(2s22p2)and forms four bonds.Because carbon uses two kinds oforbitals for bonding.2s and 2p.we might expect methane to have two kinds of C-H bonds.In fact,though,all four C-H bonds in methane are identical and are spatially oriented toward the corners of a regular tetrahedron,as shown previously in Figure 1.7.How can we explain this? An answer was provided in 1931 by Linus Pauling,who showed mathemat- ically how an s orbital and three p orbitals on an atom can combine.or hybrid ize,to form four equivalent atomic orbitals with tetrahedral orientation.Shown in 11,these tetrahedrally oriented orbitals are called sphybrids.Note h。 tetrahedron and are formed by combination of an s orbital and rical about the nudeu giving them a Hybridization and allow to other atoms. ion explains how carbon orms tetra t not why t d The sh of the hybri ansd orbital hy n an s orbital hy ne o bital f ger re lap more eft orbitals form str sn3 orbitals ybridize iously,the lobes ofa hybridize orbital.the positive plobe adds to the s tive p lobe subtracts from the s orbital.The resultant hybrid orbital is therefore unsymmetrical about the nucleus and is str ngly oriented in one direction When each of the four identical sp3 hybrid orbitals of a carbon atom over- laps with the is orbital of a hydrog en atom four identical C bonds are formed and methane results.Each C-H bond in methane has a strength of 439 kJ/mol(105 kcal/mol)and a length of 109 pm.Because the four bonds
1-6 sp3 hybrid orbitals and the Structure of methane The bonding in the hydrogen molecule is fairly straightforward, but the situation is more complicated in organic molecules with tetravalent carbon atoms. Take methane, CH4, for instance. As we’ve seen, carbon has four valence electrons (2s2 2p2) and forms four bonds. Because carbon uses two kinds of orbitals for bonding, 2s and 2p, we might expect methane to have two kinds of C–H bonds. In fact, though, all four C–H bonds in methane are identical and are spatially oriented toward the corners of a regular tetrahedron, as shown previously in Figure 1.7. How can we explain this? An answer was provided in 1931 by Linus Pauling, who showed mathematically how an s orbital and three p orbitals on an atom can combine, or hybridize, to form four equivalent atomic orbitals with tetrahedral orientation. Shown in FigUre 1.11, these tetrahedrally oriented orbitals are called sp3 hybrids. Note that the superscript 3 in the name sp3 tells how many of each type of atomic orbital combine to form the hybrid, not how many electrons occupy it. 2s 2py 2px Four tetrahedral sp3 orbitals An sp3 orbital Hybridization 2pz The concept of hybridization explains how carbon forms four equivalent tetrahedral bonds but not why it does so. The shape of the hybrid orbital suggests the answer. When an s orbital hybridizes with three p orbitals, the resultant sp3 hybrid orbitals are unsymmetrical about the nucleus. One of the two lobes is much larger than the other and can therefore overlap more effectively with an orbital from another atom when it forms a bond. As a result, sp3 hybrid orbitals form stronger bonds than do unhybridized s or p orbitals. The asymmetry of sp3 orbitals arises because, as noted previously, the two lobes of a p orbital have different algebraic signs, 1 and 2. Thus, when a p orbital hybridizes with an s orbital, the positive p lobe adds to the s orbital but the negative p lobe subtracts from the s orbital. The resultant hybrid orbital is therefore unsymmetrical about the nucleus and is strongly oriented in one direction. When each of the four identical sp3 hybrid orbitals of a carbon atom overlaps with the 1s orbital of a hydrogen atom, four identical C–H bonds are formed and methane results. Each C–H bond in methane has a strength of 439 kJ/mol (105 kcal/mol) and a length of 109 pm. Because the four bonds FigUre 1.11 Four sp3 hybrid orbitals. The four orbitals are oriented to the corners of a regular tetrahedron and are formed by combination of an s orbital and three p orbitals (red/blue). The sp3 hybrids have two lobes and are unsymmetrical about the nucleus, giving them a directionality and allowing them to form strong bonds to other atoms. Unless otherwise noted, all content on this page is © Cengage Learning. 12 chapter 1 Structure and Bonding 42912_01_Ch01_0001-0027h.indd 12 1/10/14 11:40 AM Copyright 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it
1-7 sp3HYBRID ORBITALS AND THE STRUCTURE OF ETHANE have a spccincd by sach Hc defin 1 109.5 o-callec tetrahedral angle the structure shown in FIGURE 1.12 sp3 Hybrid Orbitals and the Structure of Ethane The same kind of orbital hybridization that accounts for the methane structure also accounts for the bonding together of carbon atoms into chains and rings to make possible many millions of organic compounds.Ethane,C2H6.is the simplest molecule containing a carbon-carbon bond: HH H-C- C-H CH3CH Some representations of ethane We can picture the ethane molecule by imagining that the two carbon atoms bond to each other by o overlap of an sp hvbrid orbital from ea sp orbitals o C-C1 L ngle he tetrahe e of 109.50 The f e-2 ne.The car sphybrid orbitals.For clarity,the Unless othenwse noted.all content on this page isCenoage Leaming
have a specific geometry, we also can define a property called the bond angle. The angle formed by each H–C–H is 109.5°, the so-called tetrahedral angle. Methane thus has the structure shown in FigUre 1.12. H H H H Bond angle 109.5º Bond length C 109 pm 1-7 sp3 hybrid orbitals and the Structure of ethane The same kind of orbital hybridization that accounts for the methane structure also accounts for the bonding together of carbon atoms into chains and rings to make possible many millions of organic compounds. Ethane, C2H6, is the simplest molecule containing a carbon–carbon bond: Some representations of ethane CH H H C H H H CH H H C CH H 3CH3 H H We can picture the ethane molecule by imagining that the two carbon atoms bond to each other by s overlap of an sp3 hybrid orbital from each (FigUre 1.13). The remaining three sp3 hybrid orbitals of each carbon overlap with the 1s orbitals of three hydrogens to form the six C–H bonds. The C–H bonds in ethane are similar to those in methane, although a bit weaker—421 kJ/mol (101 kcal/mol) for ethane versus 439 kJ/mol for methane. The C–C bond is 153 pm long and has a strength of 377 kJ/mol (90 kcal/mol). All the bond angles of ethane are near, although not exactly at, the tetrahedral value of 109.5°. Ethane C C C C C C H H H H H H 153 pm sp3 carbon sp3 carbon sp3–sp3 bond 111.2° FigUre 1.12 the structure of methane, showing its 109.5° bond angles. FigUre 1.13 the structure of ethane. The carbon–carbon bond is formed by s overlap of two sp3 hybrid orbitals. For clarity, the smaller lobes of the sp3 hybrid orbitals are not shown. Unless otherwise noted, all content on this page is © Cengage Learning. 1-7 sp3 hyBrid orBitalS and the Structure of ethane 13 42912_01_Ch01_0001-0027h.indd 13 1/10/14 11:40 AM Copyright 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it
14 CHAPTER1 STRUCTURE AND BONDING PROBLEM 1.8 Draw a line-bond structure for propane,CHaCH2CH3.Predict the value of each bond angle,and indicate the overall shape of the molecule. PROBLEM 1.9 ane,a component of gasoline,into a line- d Hexane 18sp2 Hybrid Orbitals and the Structure of Ethylene The bonds we've seen in methane and ethane are called single bonds because they result from the sharing of one electron pair between bonded atoms.It was recognized nearly 150 years ago,however,that carbon atoms can also form double bonds by sharing two electron pairs between atoms or triple bonds by sharing three electron pairs.Ethylene,for instance,has the structure H2C=CH2 and contains a carbon-carbon double bond,while acetylene has the structure HC=CH and contains a carbon-carbon triple bond. How are multiple bonds described by valence bond theory?When we dis. cussed sp3 hybrid orbitals in Section 1-6,we said that the fou r valence-shell atomic or ine instea t the 2s ort 2p orbital brid o onry two or the hital ree availa and one 2p orb are unsymme cal abou on s 0 i FIGURE 1.14. e sp ne,as shown orbitals lie in a plane at angles of 120to one another,and a single unhybridized p orbital(red/blue) s perpendicular to the spe plane Top view
P r o B l e m 1 . 8 Draw a line-bond structure for propane, CH3CH2CH3. Predict the value of each bond angle, and indicate the overall shape of the molecule. P r o B l e m 1 . 9 Convert the molecular model of hexane, a component of gasoline, into a linebond structure (gray 5 C, ivory 5 H). Hexane 1-8 sp2 hybrid orbitals and the Structure of ethylene The bonds we’ve seen in methane and ethane are called single bonds because they result from the sharing of one electron pair between bonded atoms. It was recognized nearly 150 years ago, however, that carbon atoms can also form double bonds by sharing two electron pairs between atoms or triple bonds by sharing three electron pairs. Ethylene, for instance, has the structure H2C=CH2 and contains a carbon–carbon double bond, while acetylene has the structure HCCH and contains a carbon–carbon triple bond. How are multiple bonds described by valence bond theory? When we discussed sp3 hybrid orbitals in Section 1-6, we said that the four valence-shell atomic orbitals of carbon combine to form four equivalent sp3 hybrids. Imagine instead that the 2s orbital combines with only two of the three available 2p orbitals. Three sp2 hybrid orbitals result, and one 2p orbital remains unchanged. Like sp3 hybrids, sp2 hybrid orbitals are unsymmetrical about the nucleus and are strongly oriented in a specific direction so that they can form strong bonds. The three sp2 orbitals lie in a plane at angles of 120° to one another, with the remaining p orbital perpendicular to the sp2 plane, as shown in FigUre 1.14. sp2 sp2 sp2 sp2 sp2 sp2 p p 90° Side view Top view 120° FigUre 1.14 sp2 hybridization. The three equivalent sp2 hybrid orbitals lie in a plane at angles of 120° to one another, and a single unhybridized p orbital (red/blue) is perpendicular to the sp2 plane. Unless otherwise noted, all content on this page is © Cengage Learning. 14 chapter 1 Structure and Bonding 42912_01_Ch01_0001-0027h.indd 14 1/10/14 11:40 AM Copyright 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it
1-8 sp2 HYBRID ORBITALS AND THE STRUCTURE OF ETHYLENE 15 6 ach each other, they by sp -on overlap esameasg a p 1 he sha of an s 0 nd the fo a 2p-2p bond Note that the clei while the electro regions above and below a line drawn between nuclei. To comnlote the str atoms form bonds with the remaining four sp2 orbitals.Ethylene thus has a planar structure.with H-C-H and H-C-C bond angles of approximately 120.(The actual values are 117.4 for the H-C-H bond angle and 121.3 for the H-C-C bond angle.)Each C-H bond has a length of 108.7 pm and a strength of 464 kJ/mol (111 kcal/mol). p orbitals bond results from(head-on) overlap of sp2 orbitals.and ne ther part results from red/ble).The bond has egions of electron density above and below a line drawn Carbon-carbon double bond etween nucl 121.3 117A4 134 pm As you might expect.the carb n-carbon double bond in ethylene is b shorter an single bon n ethan ron ing the nucle =C bon and strength of 77 ngle b as grea s the hase overlap in the part Drawing Electron-Dot and Line-Bond Structures WORKED EXAMPLE 1.3 Commonly used in biology as a tissue preservative,formaldehyde.CH2O. contains a carbon-oxvgen double bond.Draw the line-bond structure of form aldehyde,and indicate the hybridization of the carbon atom. Strategy and error,combined Unless othenwse noted.all content on this page isCenoage Leaming
When two carbons with sp2 hybridization approach each other, they form a strong s bond by sp2–sp2 head-on overlap. At the same time, the unhybridized p orbitals interact by sideways overlap to form what is called a pi (p) bond. The combination of an sp2–sp2 s bond and a 2p–2p p bond results in the sharing of four electrons and the formation of a carbon–carbon double bond (FigUre 1.15). Note that the electrons in the s bond occupy the region centered between nuclei, while the electrons in the p bond occupy regions above and below a line drawn between nuclei. To complete the structure of ethylene, four hydrogen atoms form s bonds with the remaining four sp2 orbitals. Ethylene thus has a planar structure, with H–C–H and H–C–C bond angles of approximately 120°. (The actual values are 117.4° for the H–C–H bond angle and 121.3° for the H–C–C bond angle.) Each C–H bond has a length of 108.7 pm and a strength of 464 kJ/mol (111 kcal/mol). 121.3° C C 117.4° H H H H 134 pm 108.7 pm Carbon–carbon double bond C C sp2 sp carbon 2 carbon sp2 orbitals p orbitals bond bond bond As you might expect, the carbon–carbon double bond in ethylene is both shorter and stronger than the single bond in ethane because it has four electrons bonding the nuclei together rather than two. Ethylene has a C=C bond length of 134 pm and a strength of 728 kJ/mol (174 kcal/mol) versus a C–C length of 153 pm and a strength of 377 kJ/mol for ethane. The carbon– carbon double bond is less than twice as strong as a single bond because the sideways overlap in the p part of the double bond is not as great as the head-on overlap in the s part. Drawing electron-Dot and line-Bond Structures Commonly used in biology as a tissue preservative, formaldehyde, CH2O, contains a carbon–oxygen double bond. Draw the line-bond structure of formaldehyde, and indicate the hybridization of the carbon atom. S t r a t e g y We know that hydrogen forms one covalent bond, carbon forms four, and oxygen forms two. Trial and error, combined with intuition, is needed to fit the atoms together. FigUre 1.15 the structure of ethylene. One part of the double bond in ethylene results from s (head-on) overlap of sp2 orbitals, and the other part results from p (sideways) overlap of unhybridized p orbitals (red/blue). The p bond has regions of electron density above and below a line drawn between nuclei. W O R K E D E X A M P L E 1 . 3 Unless otherwise noted, all content on this page is © Cengage Learning. 1-8 sp2 hyBrid orBitalS and the Structure of ethylene 15 42912_01_Ch01_0001-0027h.indd 15 1/10/14 11:40 AM Copyright 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it
16 CHAPTER 1 STRUCTURE AND BONDING Solution There is only one way that two hydrogens,one carbon,and one oxygen can combine. H.CH Line-bond structure e,the carbon atom in formaldehyde is in a PROBLEM 1.10 Draw a line-bond structure for propene,CH3CH=CH2:indicate the hybridiza- tion of each carbon;and predict the value of each bond angle. PROBLEM 1.11 Draw a line-bond structure for buta-1,3-diene,H2C=CH-CH=CH2:indicate the hybridization of each carbon;and predict the value of each bond angle. PROBLEM 112 A molecular model of aspirin (acetylsalicylic acid)is shown.Identify the hybridization of each carbon atom in aspirin,and tell which atoms have lone pairs of electrons (gray =C.red =O.ivory H). eacetwanemhecacidl 19sp Hybrid Orbitals and the Structure of Acetylene In addition to forming single and double bonds by sharing two and four elec trons,respectively,carbon also can form a triple bond by shari we need a third kind of hybrid orbital,an sp hybrid.Imagine that,instead of combining with two or three p orbitals,a carbon 2s orbital hybridizes with only a single porbital.Two sp hybrid orbitals result,and two porbitals remain
S o l u t i o n There is only one way that two hydrogens, one carbon, and one oxygen can combine: Line-bond structure Electron-dot structure O C HH O C HH Like the carbon atoms in ethylene, the carbon atom in formaldehyde is in a double bond and is therefore sp2-hybridized. P r o B l e m 1 . 1 0 Draw a line-bond structure for propene, CH3CH5CH2; indicate the hybridization of each carbon; and predict the value of each bond angle. P r o B l e m 1 . 1 1 Draw a line-bond structure for buta-1,3-diene, H2C5CH–CH5CH2; indicate the hybridization of each carbon; and predict the value of each bond angle. P r o B l e m 1 . 1 2 A molecular model of aspirin (acetylsalicylic acid) is shown. Identify the hybridization of each carbon atom in aspirin, and tell which atoms have lone pairs of electrons (gray 5 C, red 5 O, ivory 5 H). Aspirin (acetylsalicylic acid) 1-9 sp hybrid orbitals and the Structure of acetylene In addition to forming single and double bonds by sharing two and four electrons, respectively, carbon also can form a triple bond by sharing six electrons. To account for the triple bond in a molecule such as acetylene, H–CC–H, we need a third kind of hybrid orbital, an sp hybrid. Imagine that, instead of combining with two or three p orbitals, a carbon 2s orbital hybridizes with only a single p orbital. Two sp hybrid orbitals result, and two p orbitals remain Unless otherwise noted, all content on this page is © Cengage Learning. 16 chapter 1 Structure and Bonding 42912_01_Ch01_0001-0027h.indd 16 1/10/14 11:40 AM Copyright 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it